# Analysis of Obstacle based Probabilistic RoadMap Method using Geometric Probability

## TL;DR

This paper evaluates the success probability of obstacle-based probabilistic roadmap planners (OBPRM) in robot motion planning, revealing that success likelihood depends on the surface area of obstacles in the configuration space.

## Contribution

It introduces a geometric probability analysis of OBPRM, providing insights into how obstacle surface area influences sampling success in high-dimensional spaces.

## Key findings

- Success probability is proportional to obstacle surface area.
- Analysis helps improve sampling strategies in narrow passages.
- Provides a theoretical foundation for heuristic improvements.

## Abstract

Sampling based planners have been successful in robot motion planning, with many degrees of freedom, but still remain ineffective in the presence of narrow passages within the configuration space. There exist several heuristics, which generate samples in the critical regions and improve the efficiency of probabilistic roadmap planners. In this paper, we present an evaluation of success probability of one such heuristic method, called obstacle based probabilistic roadmap planners or OBPRM, using geometric probability theory. The result indicates that the probability of success of generating free sample points around the surface of the $n$ dimensional configuration space obstacle is directly proportional to the surface area of the obstacles.